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From: Osher Doctorow on 6 Aug 2010 20:11
From Osher Doctorow

In the last few posts, I mentioned that the 5 dimensions ordinarily or
maximally used (L, T, M, theta, Q, respectively length (space), time,
mass, temperature, electric charge) if doubled yield 10 dimensions as
with Superstring Theory, and one possibility that I gave (but did not
postulate as "the" answer) is to pair dimensions like L with their
multiplicative inverses L^(-1). However, one reason for not doing
this is the fact that fundamental dimensions form an abelian
(commutative) group under "multiplication", so inverses are not
separately fundamental from the original dimensions.

A different direction is a clue given by Electrostatic Repulsion of
identical charges (+, + as for two protons, or -, - as for two
electrons) compared to Electrostatic Attraction of opposite charges
(+, - as for proton vs electron).

The usual dimensional analysis symbol for Electric Charge is Q, so we
now distinguish between:

1) Q1 = (definition) Attractive Charge, which may be dependent on
comparing internal and external scenarios or objects.

2) Q2 = (definition) Repulsive Charge, which may be dependent on
comparing internal and external scenarios or objects.

At first glance, it appears that Q1 and Q2 correctly describe
respectively Attraction and Repulsion of Charges but not the process
by which these Attractions or Repulsions occur, since that process
depends on which objects (electrons, protons) are involved. They
therefore seem to lack simplicity or intuition in such respects.

Yet there is arguably an advance in describing Charges as Attractive
or Repulsive, since that describes what the Charges are actually doing
spatially and temporally, unlike the original Q that does not do
that. So there is a good argument for Electric Charge as consisting
of two Dimensions of Charge, Q1 (Attractive Charge) and Q2 (Repulsive
Charge), although Q could be used if there is no particular interest
in distinguishing them or if confusion is unlikely.

If we could do this pairing with all the remaining dimensions L, T, M,
theta (temperature), then we would have 10 Fundamental Dimensions.
We already know that Attraction and Repulsion themselves are space-
time (as well as related to other dimensions), and that they have
opposite directions which for example for spherical objects are normal
to the center of the sphere and to the surface of the sphere. So,
analogously with Q, I define for bounded objects:

3) L1 = Attractive Length (Length as a Displacement vector toward an
object A, e.g. spherical)
4) L2 = Repulsive Length (Length as a Displacement vector away from an
object A, e.g. spherical)

Osher Doctorow
From: Osher Doctorow on 6 Aug 2010 20:18
From Osher Doctorow

Since an expanding or contracting object moves oppositely in space but
also through time, and similarly for repelling vs attracting objects,
we can arguably define:

1) T1 = time in the process of Attraction or Contraction
2) T2 = time in the process of Repulsion or Expansion

We thus have 6 Fundamental Dimensions from "pairing" opposites:

3) Q1, Q2, L1, L2, T1, T2

and two remaining "unpaired" Fundamental Dimensions whose pairs we may
seek:

4) M, theta (temperature).

This gives us 8 Fundamental Dimensions at present.

Osher Doctorow
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